关于正形置换的构造  

On the construction of orthomorphic permutations

作　　者：周建钦[1] 

机构地区：[1]安徽工业大学计算机学院,安徽马鞍山243002

出　　处：《华中科技大学学报（自然科学版）》2007年第2期40-42,46,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60473142);安徽省教育厅自然科学基金资助项目(2006KJ238B)

摘　　要：基于正形置换的定义,给出一个实用的正形置换构造算法及其应用,得到全部16次正形置换的计数为244 744 192;通过求解有限域F2m上矩阵的逆矩阵,给出一个简捷的F2m上与一个置换对应的置换多项式构造方法,得到了有限域F42上的全部正形置换多项式,并且证明其多项式次数均小于14.证明了有限域F2m上置换多项式的多项式次数均小于2m-1.Orthomorphic permutations are important in block ciphers designs. Based on the definition of orthomorphic permutation, a practical method is presented to generate all orthomorphic permutations over F2^m, and it was verified that the number of all orthomoriphic permutations over F2^4 is 244 744 192. By the inverse matrix of a matrix over finite field F2^n, a brief method was presented to generate a permutation polynomial corresponding to every permutation over F2^m, and all orthomotheriphic permutation polynomials over F2^4 were analysed and found to be of order less than 14. It was proved that the order of permutation polynomial over F2^m is less than 2^m- 1.

关 键 词：分组密码 正形置换 多项式 

分 类 号：O151[理学—数学] TN911.22[理学—基础数学]